Let's misuse the end-to-end principle for purposes of airport security. For passing TSA balrogs in the minimal amount of time, observe that if the time between arriving at the airport and boarding the aeroplane is great, it doesn't matter how swiftly you pass through security -- you aren't getting on the plane any sooner. (So this doesn't quite apply if you are hurrying to catch your flight, because a security delay might make you miss it.) Between entering the airport system and exiting the airport (into the aeroplane), you are just waiting for, basically, a fixed amount of time.
Should you remove your shoes and have them scanned? After all, the nice secure people ask you to. But generally the longest queues in airports are those feeding into security. It's reasonable to expect some delay D caused by removing your shoes, which affects everyone behind you in line (not necessarily equal to the extra time it takes to remove your shoes). On the other hand, not removing your shoes and walking through might get you thoroughly searched for some time T, with some probability p. One might think that pT > D. (Plus there is the risk of privacy invasion. You could care. I always thought there should be a classic arcade game spoof called Privacy Invaders, but that's another story.) But now, you're not holding up anyone behind you in line, since either you receive special treatment or you just pass through. This helps everyone else behind you go through faster. You might be slowed, but it doesn't matter! You don't board the aeroplane any sooner!
Most likely, I've neglected some critical factor like the baggage in the X-ray machine that completely breaks my oversimplified model. Also, if no one takes off their shoes, there becomes a queue for special treatment, which breaks the model too. But the conclusion is:
(1) If you're in a hurry, you should take off your shoes. You pass through security faster.
(2) If you're not, you shouldn't, but expect a longer delay. Everyone else passes through security faster.
So the immediately slower action is better for the person in a hurry. (Assuming pT > D; if that wasn't true, you would never want to take off your shoes.)
Those nice secure people are just hoarsening their voices for nothing. Hooray for Saltzer!